Investigation On The Energy Levels And The Fine Structure Of Boron-like Atoms

With the aids of the angular momentum coupling theory, the diagonal sum rule and the irreducible tensor theory, a formulism for calculating the matrix elements of Boron-like atoms'non-relativistic Hamilton between the Racah wave functions have been derived. Based on this approach, the non-relativistic energies of Boron-like atoms in the ground and the first excited states have been obtained. Afterwards, using the spherical tensor form of many-electron atom Hamilton and the irreducible tensor theory, the relativistic and fine-structure energy correction to the non-relativistic energy of Boron-like atoms in the ground and the first excited states have been further investigated. A theoretically analytic way has been given as to the calculation of all the radial integrations and spin summations, which concern interactions such as orbit-orbit, spin-orbit, spin-spin and spin-other-orbit. Therefore, the whole process of calculating the many- electron atom energy structures has been explicitly revealed and the results are relatively precise and satisfactory. This paper is divided into five parts as follows.In Chapter one, the fundamental qualities of angular momentum and the angular momentum coupling theory has been introduced, which lays the theoretic foundations of studying the non-relativistic energies, the relativistic and fine-structure energy corrections of Boron-like atoms.In Chapter Two, aided by the angular momentum coupling theory, the items of orbit-orbit, spin-orbit, spin-spin and spin-other-orbit in the many-electron atom Hamilton have all been transformed into spherical tensor forms, which have the advantage that the radial, angular and spin parts of the Hamilton can be completely separated and so the matrix elements can be easily worked out. The angular and spin matrix elements can be obtained using the irreducible tensor theory.In Chapter Three, based on the diagonal sum rule, a formulism for calculating the matrix elements of Boron-like atoms'non-relativistic Hamilton between the Racah wave functions have been derived. After all the angular integrations and spin summations completed, the needed parameters in the non-relativistic wave functions have been acquired using the variational method and so the functions themselves have been established in this way. And the non-relativistic energies for boron-like atoms in the ground and first excited states have been obtained.In Chapter Four, using the irreducible tensor theory, an expression for the relativistic energy correction to the non-relativistic energies of boron-like atoms in the ground and first excited states has been established, which includes mass correction, Darwin corrections, spin-spin-contact and orbit-orbit corrections. We've completed all the angular integrations and spin summations involved and make the final expression for relativistic correction in a combination of radial integrations.In Chapter Five, an approach to calculate the fine-structure energies of boron-like atoms in the ground and first excited states has been provided. Concretely speaking, using the irreducible tensor theory, we deuced the formulism for fine-structure energies of boron-like atoms in the ground and first excited states, which involves spin-orbit, spin-spin and spin-other-orbit interactions; completing all the angular integrations and spin summations needed, we make the final expression for fine-structure energies of boron-like atoms in the ground and first excited states in a combination of radial integrations. Afterwards, employing the wave functions we got in Chapter Three, we accomplished all the radial integrations and so obtained the fine-structure energies. The results show that the errors for the total energies all less than 0.4%, yet the errors for splitting are a little striking, which is mainly caused by the inaccuracy of the wave functions.